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Horizontal Hyperbolas

Horizontal Hyperbolas
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2017-04-30 23:04
Coordinate GeometryTransformationGeometric Construction
In collections Conics Investigation
This example demonstrates the geometric properties of horizontal hyperbolas, including special points such as foci and vertices, and the concept of similarity transformation. By adjusting parameters, one can observe changes in the shape of the hyperbola. The construction uses GeoGebra commands such as points, lines, and loci. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Numeric a(3.1)
  2. Numeric b(2.95)
  3. Numeric h(0.4)
  4. Numeric k(-0.25)
  5. (h, k)
  6. sqrt(a^(2) + b^(2))
  7. (h + c, k)
  8. (h - c, k)
  9. (h + a, k)
  10. (h - a, k)
  11. (x - 3)^(2) / 2^(2) + (y - 4)^(2) / 3^(2) = 1
  12. Boolean boo1(false)
  13. Boolean boo2(false)
  14. (x - h)^(2) / a^(2) - (y - k)^(2) / b^(2) = 1
  15. (x - 3)^(2) / 2^(2) - (y - 2)^(2) / 1^(2) = 1
  16. (x - 5)^(2) / 3^(2) - (y + 4)^(2) / 2^(2) = 1
  17. y = (b / a * (x - h)) + k
  18. y = (((-b)) / a * (x - h)) + k